Mesoscale damping and stiffening in silicon microbeams: A heat-map study using a memory-dependent Green-Naghdi model

Abstract

By investigating the vibration characteristics of a generalized thermoelastic silicon microbeam in the context of crossover thermoelasticity, this study opens up novel opportunities that assumes the temporally crossover of thermal conduction with acceleration, in the sense that the thermal conductivity starts low and becomes relatively high eventually. A novel spatiotemporal nonlocal elasticity theory is proposed by taking into account one dynamical scalar nonlocal kernel. In line with the theory, an isotropic nonlocal elasticity model of the Klein-Gordon type is formulated, incorporating both a characteristic internal length scale and an essential internal time scale parameter. The Euler-Bernoulli assumption is proposed subject to the influence of the prescribed temperature on the upper surface of the beam. Heat transport process for the present problem is deigned in the context of modified Green-Naghdi models. Finite Fourier sine transform and the Laplace transform mechanism have been adopted to determine the solution of the governing equations. However, the Laplace transform is then numerically inverted using a method based on the method of Zakian. For numerous modified Green-Naghdi models, thermoelastic vibrations for thermal moment and lateral deflection have been estimated and the superiority of the modified models over the conventional Green-Naghdi model is analyzed. The amplification due to the spatiotemporal nonlocal parameters and the relaxation parameter is also reported. The significance of memory response and various kernel function is analyzed too. In conclusion, it is also investigated that Silicon beam exhibits a dependence on size and nonlocal behavior in heat conduction at the nano-/microscale, where the main carriers of heat travels anomalously instead of through the usual diffusive process within the medium.